A Finite-Time Trajectory-Tracking Method for State-Constrained Flexible Manipulators Based on Improved Back-Stepping Control

In order to solve the trajectory-tracking-control problem of the state-constrained flexible manipulator systems, a finite-time back-stepping control method based on command filtering is presented in this paper. Considering that the virtual signal requires integration in each step, which will lead to high computational complexity in the traditional back-stepping, the finite-time command filter is used to filter the virtual signal and to obtain the intermediate signal in finite time, to thus reduce the computational complexity. The compensation mechanism is used to eliminate the error generated by the command filter. Furthermore, the adaptive estimation method is introduced to approach the uncertainty of the state-constrained flexible manipulator system. Then, the Lyapunov function is used to prove that the tracking error of the system can be stabilized in a sufficiently small origin neighborhood within a finite time. The simulation of a single rod flexible manipulator system demonstrates the effect of the proposed approach